A definition of complexity for self-gravitating systems is introduced in [1]}
which is based on the work developed by Lopez-Ruiz and his collaborators [2]}.
In this definition, probability distribution which appear in the definition of entropy
and information is replaced by energy density of the
fluids, which has been justified by the argument that this physical quantity is
related to the probability of finding some particles at given specified location
inside the star, or it proved difficult to suggest a better alternative from the
available physical quantities. Nevertheless, this definition has some important
drawbacks, as it only encompasses the role of energy density whereas other
physical parameters like pressure isotropy or anisotropy which are expected
to play an important role in structure formation of a system are completely
ignored. In order to avoid these drawbacks, an entirely new definition of complexity [3]} has
been proposed for spherically symmetric and static self-gravitating source. It is
devised on the basic assumption that less complex systems correspond to the fluid
configurations with homogeneous energy density and isotropic pressure.
Such distributions are assigned with zero degree of complexity factor
which appears in orthogonal splitting of Riemann tensor. Herrera and his collaborators extended this concept
of complexity from static to non-static scenario, where they consider not only the complexity factor
of structure of fluid configuration but also discuss the conditions of minimum
complexity of evolutionary patterns [4]}. For an axially symmetric static source,
they explored three different complexity factors and found that all the three factors vanish for simplest fluid configuration [5]}.
The significance of this definition motivated the researchers to explore
it for different scenarios. Herrera et al. extended this fascinating concept to the vacuum solutions
with the help of the Bondi metric which covers a huge number of spacetimes like
Minkowski spacetime, the static Weyl
metrics, gravitationally
radiating metrics, non radiative and non static metrics [6]}, while Casadio et al.
studied isotropization and change of complexity
employing gravitational decoupling approach for
a static and spherically symmetric system [7]}.
In [8]}, the effects of electric charge has been incorporated and complexity factor has been
analyzed. They have found that electromagnetic field has considerable impacts on the complexity
of a cosmological structure. The same authors discussed the complexity of cylindrically symmetric static source in [9]}.
